When an airport has tie downs listed on their official FAA record, who is responsible for the ropes/chains. Is there any federal regulation or legal precedent for this or is it a case-by-case determination based on the FBO policy?
I read this as "there is a place to park your plane for a while and tie it down if you are so inclined." I do not expect the airport to provide the chains or ropes. Some will, but small town or village airports are barely maintained and nobody is thinking about how to make life better for transient airplane owners. If you intend to park and leave the plane for any length of time you should be carrying your own means of physically securing the airplane to the ground.
It's the pilot's responsibility to ensure the plane is safe.